Moving averages are one of the most popular and easy to use tools available to the technical analyst. They smooth a data series and make it easier to spot trends, something that is especially helpful in volatile markets. They also form the building blocks for many other technical indicators and overlays.

The two most popular types of moving averages are the Simple Moving Average (SMA) and the Exponential Moving Average (EMA). They are described in more detail below.

Simple Moving Average (SMA)
(Click here to see a live example of a Simple Moving Average)

A simple moving average is formed by computing the average (mean) price of a security over a specified number of periods. While it is possible to create moving averages from the Open, the High, and the Low data points, most moving averages are created using the closing price. For example: a 5-day simple moving average is calculated by adding the closing prices for the last 5 days and dividing the total by 5.

The calculation is repeated for each price bar on the chart. The averages are then joined to form a smooth curving line - the moving average line. Continuing our example, if the next closing price in the average is 15, then this new period would be added and the oldest day, which is 10, would be dropped. The new 5-day simple moving average would be calculated as follows:

Over the last 2 days, the SMA moved from 12 to 13. As new days are added, the old days will be subtracted and the moving average will continue to move over time.

In the example above, using closing prices from Eastman Kodak (EK), day 10 is the first day possible to calculate a 10-day simple moving average. As the calculation continues, the newest day is added and the oldest day is subtracted. The 10-day SMA for day 11 is calculated by adding the prices of day 2 through day 11 and dividing by 10. The averaging process then moves on to the next day where the 10-day SMA for day 12 is calculated by adding the prices of day 3 through day 12 and dividing by 10.

The chart above is a plot that contains the data sequence in the table. The simple moving average begins on day 10 and continues.

This simple illustration highlights the fact that all moving averages are lagging indicators and will always be "behind" the price. The price of EK is trending down, but the simple moving average, which is based on the previous 10 days of data, remains above the price. If the price were rising, the SMA would most likely be below. Because moving averages are lagging indicators, they fit in the category of trend following indicators. When prices are trending, moving averages work well. However, when prices are not trending, moving averages can give misleading signals.

Exponential Moving Average (EMA)
(Click here to see a live example of an Exponential Moving Average)

In order to reduce the lag in simple moving averages, technicians often use exponential moving averages (also called exponentially weighted moving averages). EMA's reduce the lag by applying more weight to recent prices relative to older prices. The weighting applied to the most recent price depends on the specified period of the moving average. The shorter the EMA's period, the more weight that will be applied to the most recent price. For example: a 10-period exponential moving average weighs the most recent price 18.18% while a 20-period EMA weighs the most recent price 9.52%. As we'll see, the calculating and EMA is much harder than calculating an SMA. The important thing to remember is that the exponential moving average puts more weight on recent prices. As such, it will react quicker to recent price changes than a simple moving average. Here's the calculation formula.

Exponential Moving Average Calculation

Exponential Moving Averages can be specified in two ways - as a percent-based EMA or as a period-based EMA. A percent-based EMA has a percentage as it's single parameter while a period-based EMA has a parameter that represents the duration of the EMA.

For a percentage-based EMA, "Multiplier" is equal to the EMA's specified percentage.
For a period-based EMA, "Multiplier" is equal to 2 / (1 + N) where N is the specified number of periods.

For example, a 10-period EMA's Multiplier is calculated like this:

This means that a 10-period EMA is equivalent to an 18.18% EMA.

Below is a table with the results of an exponential moving average calculation for Eastman Kodak. For the first period's exponential moving average, the simple moving average was used as the previous period's exponential moving average (yellow highlight for the 10th period). From period 11 onwards, the previous period's EMA was used. The calculation in period 11 breaks down as follows:

*The 10-period simple moving average is used for the first calculation only. After that the previous period's EMA is used.
(Click here to download this table as an Excel spreadsheet.)

Note that, in theory, every previous closing price in the data set is used in the calculation of each EMA that makes up the EMA line. While the impact of older data points diminishes over time, it never fully disappears. This is true regardless of the EMA's specified period. The effects of older data diminish rapidly for shorter EMA's. than for longer ones but, again, they never completely disappear.

I hope this helps... If not, let me know and I will simply some more...

[QUOTE=Commando Trader;11883]The easiest answer to your questions is get a charting program that does the calculation for you based on the number of days and choosing the close, open, high, or average price.

But, if you want to do it by hand, you will need to do the following...

Moving Averages - Part 1

You are Here: Chart School > What is TA? > Indicator Analysis > Moving Averages - Part 1

Moving averages are one of the most popular and easy to use tools available to the technical analyst. They smooth a data series and make it easier to spot trends, something that is especially helpful in volatile markets. They also form the building blocks for many other technical indicators and overlays.

The two most popular types of moving averages are the Simple Moving Average (SMA) and the Exponential Moving Average (EMA). They are described in more detail below.

Simple Moving Average (SMA)
(Click here to see a live example of a Simple Moving Average)

A simple moving average is formed by computing the average (mean) price of a security over a specified number of periods. While it is possible to create moving averages from the Open, the High, and the Low data points, most moving averages are created using the closing price. For example: a 5-day simple moving average is calculated by adding the closing prices for the last 5 days and dividing the total by 5.

The calculation is repeated for each price bar on the chart. The averages are then joined to form a smooth curving line - the moving average line. Continuing our example, if the next closing price in the average is 15, then this new period would be added and the oldest day, which is 10, would be dropped. The new 5-day simple moving average would be calculated as follows:

Over the last 2 days, the SMA moved from 12 to 13. As new days are added, the old days will be subtracted and the moving average will continue to move over time.

In the example above, using closing prices from Eastman Kodak (EK), day 10 is the first day possible to calculate a 10-day simple moving average. As the calculation continues, the newest day is added and the oldest day is subtracted. The 10-day SMA for day 11 is calculated by adding the prices of day 2 through day 11 and dividing by 10. The averaging process then moves on to the next day where the 10-day SMA for day 12 is calculated by adding the prices of day 3 through day 12 and dividing by 10.

The chart above is a plot that contains the data sequence in the table. The simple moving average begins on day 10 and continues.

This simple illustration highlights the fact that all moving averages are lagging indicators and will always be "behind" the price. The price of EK is trending down, but the simple moving average, which is based on the previous 10 days of data, remains above the price. If the price were rising, the SMA would most likely be below. Because moving averages are lagging indicators, they fit in the category of trend following indicators. When prices are trending, moving averages work well. However, when prices are not trending, moving averages can give misleading signals.

Exponential Moving Average (EMA)
(Click here to see a live example of an Exponential Moving Average)

In order to reduce the lag in simple moving averages, technicians often use exponential moving averages (also called exponentially weighted moving averages). EMA's reduce the lag by applying more weight to recent prices relative to older prices. The weighting applied to the most recent price depends on the specified period of the moving average. The shorter the EMA's period, the more weight that will be applied to the most recent price. For example: a 10-period exponential moving average weighs the most recent price 18.18% while a 20-period EMA weighs the most recent price 9.52%. As we'll see, the calculating and EMA is much harder than calculating an SMA. The important thing to remember is that the exponential moving average puts more weight on recent prices. As such, it will react quicker to recent price changes than a simple moving average. Here's the calculation formula.

Exponential Moving Average Calculation

Exponential Moving Averages can be specified in two ways - as a percent-based EMA or as a period-based EMA. A percent-based EMA has a percentage as it's single parameter while a period-based EMA has a parameter that represents the duration of the EMA.

For a percentage-based EMA, "Multiplier" is equal to the EMA's specified percentage.
For a period-based EMA, "Multiplier" is equal to 2 / (1 + N) where N is the specified number of periods.

For example, a 10-period EMA's Multiplier is calculated like this:

This means that a 10-period EMA is equivalent to an 18.18% EMA.

Below is a table with the results of an exponential moving average calculation for Eastman Kodak. For the first period's exponential moving average, the simple moving average was used as the previous period's exponential moving average (yellow highlight for the 10th period). From period 11 onwards, the previous period's EMA was used. The calculation in period 11 breaks down as follows:

*The 10-period simple moving average is used for the first calculation only. After that the previous period's EMA is used.
(Click here to download this table as an Excel spreadsheet.)

Note that, in theory, every previous closing price in the data set is used in the calculation of each EMA that makes up the EMA line. While the impact of older data points diminishes over time, it never fully disappears. This is true regardless of the EMA's specified period. The effects of older data diminish rapidly for shorter EMA's. than for longer ones but, again, they never completely disappear.

I hope this helps... If not, let me know and I will simply some more...

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